Journal of Materials Science

, 42:9894 | Cite as

Experimental and theoretical investigation of nonlinear viscoelastic polyurethane systems

  • Michael Johlitz
  • Holger Steeb
  • Stefan Diebels
  • Anthippi Chatzouridou
  • Jan Batal
  • Wulff Possart


The non-linear viscoelastic behaviour of a polyurethane (PUR) network is determined by continuous uniaxial tension tests and stepwise relaxation tests. Following the concept of internal variables on the modelling side, the finite Neo-Hookean material model combined with linear evolution equations for the internal variables is applied to include the time-dependence caused by viscoelasticity. The parameters are identified by an evolution strategy combined with a non-linear finite element analysis which solves the boundary value problem given by the specimen geometry and testing conditions. In conclusion, the combination of the described experiments and modelling provides a full description of the mechanical behaviour of the given PUR.


Constant Strain Rate Uniaxial Tension Test Maxwell Element Aluminium Stripe Dogbone Specimen 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors are grateful to the DFG (German Science Foundation—Deutsche Forschungsgemeinschaft) for financial support through the grant numbers Di 430/5-1 and Po 577/15-1.


  1. 1.
    Amin AFMS, Alam MS, Okui Y (2002) Mech Mater 34:75CrossRefGoogle Scholar
  2. 2.
    Amin AFMS, Alam MS, Okui Y (2003) J Test Eval 31(6):524Google Scholar
  3. 3.
    Amin AFMS, Lion A, Sekita S, Okui Y (2006) Int J Plasticity 22:1610CrossRefGoogle Scholar
  4. 4.
    Batal J (2002) Möglichkeiten zur Messung der Haftkraft einer strukturierten Polymeroberfläche. Universität des Saarlandes, SaarbrückenGoogle Scholar
  5. 5.
    Batal J (2004) Haftkraftmessung an biomimetisch strukturierten Polymeroberflächen. Universität des Saarlandes, SaarbrückenGoogle Scholar
  6. 6.
    Braess D (1997) Finite Elemente. Springer, BerlinGoogle Scholar
  7. 7.
    Bergstrom JS, Boyce MC (1998) J Mech Phys Solids 56(5):931CrossRefGoogle Scholar
  8. 8.
    Boyce MC, Arruda EM (2000) Rubber Chem Technol 73:504Google Scholar
  9. 9.
    Bergstrom JS, Boyce MC (2000) Mech Mater 32:627CrossRefGoogle Scholar
  10. 10.
    Bergstrom JS, Boyce MC (2001) Macromolecules 34(3):614CrossRefGoogle Scholar
  11. 11.
    Bergstrom JS, Boyce MC (2001) Mech Mater 33:523CrossRefGoogle Scholar
  12. 12.
    Coleman B, Noll W (1963) Arch Ration Mech Anal 13:167CrossRefGoogle Scholar
  13. 13.
    Diebels S, Ellsiepen P, Ehlers W (1999) Tech Mech 19:19Google Scholar
  14. 14.
    Dzierza W (1978) J Appl Polym Sci 22:1331CrossRefGoogle Scholar
  15. 15.
    Ehlers W, Ellsiepen P, PANDAS: Ein FE-System zur Simulation von Sonderproblemen der Bodenmechanik. Ernst & Sohn, Berlin 1998, p 400Google Scholar
  16. 16.
    Ellsiepen P, Hartmann S (2001) Int J Numer Meth Eng 51:679CrossRefGoogle Scholar
  17. 17.
    Furukawa T, Yagawa G (1997) Int J Numer Meth Eng 40:1071CrossRefGoogle Scholar
  18. 18.
    Haupt P (2000) Continuum mechanics and theory of materials. Springer, BerlinGoogle Scholar
  19. 19.
    Haupt P, Lion A, Backhaus E (2000) Int J Solids Struct 37:3633CrossRefGoogle Scholar
  20. 20.
    Haupt P, Lion A (2002) Acta Mech 159:87CrossRefGoogle Scholar
  21. 21.
    Khan AS, Lopez-Pamies O, Kazmi R (2006) Int J Plasticity 22:581CrossRefGoogle Scholar
  22. 22.
    Keck J (1998) Zur Beschreibung finiter Deformationen von Polymeren, Experimente, Modellbildung, Parameteridentifikation und Finite-Elemente-Formulierung. Bericht-Nr. I-5 des Instituts für Mechanik (Bauwesen), StuttgartGoogle Scholar
  23. 23.
    Kröner E (1960) Arch Ration Mech Anal 4:273CrossRefGoogle Scholar
  24. 24.
    Laiarinandrasana L, Piques R, Robisson A (2003) Int J Plasticity 19:977CrossRefGoogle Scholar
  25. 25.
    Lee EH, Liu DT (1967) J Appl Phys 38:19CrossRefGoogle Scholar
  26. 26.
    Lee EH (1969) J Appl Mech 36:1Google Scholar
  27. 27.
    Leterrier Y, G’sell C (1988) J Mater Sci 23:4209CrossRefGoogle Scholar
  28. 28.
    Lion A (1996) Continuum Mech Therm 8:153Google Scholar
  29. 29.
    Lion A (1997) Acta Mech 123:1CrossRefGoogle Scholar
  30. 30.
    Lion A (1999) Rubber Chem Technol 72: 410Google Scholar
  31. 31.
    Lion A, Thermomechanik von Elastomeren. Bericht-Nr. 1/2000 des Instituts für Mechanik, Kassel 2000Google Scholar
  32. 32.
    Lubliner J (1985) Mech Res Commun 12:93CrossRefGoogle Scholar
  33. 33.
    Mahnken R (1996) Int J Plasticity 12:451CrossRefGoogle Scholar
  34. 34.
    Miehe C, Keck J (2000) J Mech Phys Solids 48:323CrossRefGoogle Scholar
  35. 35.
    Miehe C, Göktepe S, Lulei F (2004) J Mech Phys Solids 52:2617CrossRefGoogle Scholar
  36. 36.
    Miehe C, Göktepe S (2005) J Mech Phys Solids 53:2231CrossRefGoogle Scholar
  37. 37.
    Göktepe S, Miehe C (2005) J Mech Phys Solids 53:2259CrossRefGoogle Scholar
  38. 38.
    Mooney M (1940) J Appl Phys 11:582CrossRefGoogle Scholar
  39. 39.
    Müller D, Hartmann G (1989) J Eng Mater Technol 111:299CrossRefGoogle Scholar
  40. 40.
    Partom Y (1983) Polym Eng Sci 23:849CrossRefGoogle Scholar
  41. 41.
    Randrianantoandro H, Nicolai T, Duront D, Prochazka F (1997) Macromolecules 30:5893CrossRefGoogle Scholar
  42. 42.
    Rechenberg I (1973) Evolutionsstrategie: optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, StuttgartGoogle Scholar
  43. 43.
    Reese S (2001) Thermomechanische Modellierung gummiartiger Polymerstrukturen. F01/4 Institut für Baumechanik und Numerische Mechanik, HannoverGoogle Scholar
  44. 44.
    Reese S, Govindjee S (1998) Mech Time-Depend Mater 1:357CrossRefGoogle Scholar
  45. 45.
    Reese S, Govindjee S (1998) Int J Solids Struct 35:3455CrossRefGoogle Scholar
  46. 46.
    Reese S, Wriggers P (1997) Comput Methods Appl Mech Eng 148:279CrossRefGoogle Scholar
  47. 47.
    Reese S, Wriggers P (1999) In: Dorfmann A, Muhr A (eds) Modelling of the thermomechanical material behaviour of rubber-like polymers–micromechanical motivation and numerical simulation. Proceedings of the First European Conference on Constitutive Models for Rubber, Rotterdam, p 13Google Scholar
  48. 48.
    Rivlin RS (1947) Phil Trans R Soc Lond A 241:379CrossRefGoogle Scholar
  49. 49.
    Scheday G, Theorie und Numerik der Parameteridentifikation von Materialmodellen der finiten Elastizität und Inelastizität auf der Grundlage optischer Feldmessmethoden. Bericht-Nr. I-11 des Instituts für Mechanik (Bauwesen), Stuttgart 2003Google Scholar
  50. 50.
    Schwefel HP (1995) Evolution and optimum seeking. Wiley, New YorkGoogle Scholar
  51. 51.
    Tallec PL, Kaiss A, Rahier C (1994) Int J Numer Meth Eng 37:1159CrossRefGoogle Scholar
  52. 52.
    Treloar LR (1976) Proc R Soc Lond A 351:301Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Michael Johlitz
    • 1
  • Holger Steeb
    • 1
  • Stefan Diebels
    • 1
  • Anthippi Chatzouridou
    • 1
  • Jan Batal
    • 2
  • Wulff Possart
    • 2
  1. 1.Chair of Applied MechanicsSaarland UniversitySaarbrückenGermany
  2. 2.Chair of Adhesion and Interphases in PolymersSaarland UniversitySaarbrückenGermany

Personalised recommendations